Why didn't the Romans conquer Ireland they failed to conquer Scotland?
There was not much of a point. The Roman Empire was only really interested in the fertile lowlands of England, roughly from York to Exeter, which served among other things to supply the continental Rhineland armies with grain and other foodstuffs. Even a good part of the Britannic province, all the Pennine and Welsh mountains, should be regarded essentially as buffers. Archaeology actually informs us that Ireland was at a rather low ebb, with respect to population and prosperity, during the Roman period, and the Romans can't have seen much of anything worth the trouble there. I have argued that there is evidence in Irish legend for at least one major Roman raid into Ireland that reached as far as Athenry, though I'm afraid my argument is long and complex and part of something quite different (History of Britain 407–597, book 6, ch.3, especially section 10 - HISTORY OF BRITAIN, 407-597, by Fabio P. Barbieri ). But whether or not I am correct, it is certain that the Romans could have entered Ireland and Scotland and conquered them. Then what? How would the empire even feed itself, in such scarcely populated and infertile territories? Before the industrial revolution, these countries were on the edge of the world.
Hidden beneath your question is another question-as to whether reaching a point of contentment equates with the "failure" to proceed. When the Romans reached the line of what became Hadrian's wall they also reached in that respect and what we might call the Point of Contentment. The ancient Scots did not "beat" the Romans. The Romans just cam up against "the law of diminishing returns" and saw their position in terms of the question of rewards versus effort. In short, they simply didn't think it worth going any further.
Something I have not (so far) heard from anywhere else: given their brush with Hannibal some three centuries earlier the Romans under Hadrian were only too aware of how snow and ice can defeat an invading army. If anything "defeated" the Romans in Scotland there's a fair chance it was the weather alone.
Ireland. There is now continually emerging significant evidence of a Roman presence in at least the central-eastern coastal areas of Ireland. Along with that and in time may arise evidence that their attitude to Ireland at that time may have been much the same as it was to Scotland. For certain, the Scots and Irish having so much in common the Romans may have viewed Ireland itself in the same light.
Empire building is an expensive process as is maintaining an Empire. There was no economic or strategic return for invading Ireland, it did not present a threat or an opportunity to the Romans so they left it alone and let locals trade with it from Wales, Scotland, Cornwall, NW Britain, France, Brittany and the Basque Country.
Rome invaded Scotland a number of times and built both Hardians Wall and then quite a bit further north Antoines Wall. It is arguable that Rome's influence in Scotland was definite and firm right up to the river Tay in Scotland for hundreds of years.
Life North of the Tay is different. It might be why the Highland line runs from Aberdeen or Wick to near Oban (its a bit ropey and depends on the conversation, North Easterns have it in for everyone it seems) and people from below that line are according to family lore are, "Southerns". Romans rarely went north and neither did anyone else for centuries, it remained the land of Vikings and Clans until the modern era, it declined with the last of the Stuarts and the failed rebellions and in NE Scotland with the demise of the Old Norse people by the early 20C Scotland was finally a single people (sort of).
South of the Highland line the Romans would have been able to extract an economic return from the land in the form of cropping, mining, dried fish etc. They would also have been able to develop a secure buffer for the British provinces. In lowland Scotland they could move their troops effectively and execute their strategic and military superiority, North of the Tay this would have been much harder.
So the Romans did what was good for the Romans and they conquered, controlled and settled land only where it was economically viable to do so as the local Roman leaders had to provide a return each year to Rome.
The Romans made at least two serious attempts to conquer Scotland. The first under Agricolla in 84 AD and the second under Septimus Severus in 208 - 210 AD . Both times the Scots / Picts got lucky . They inflicted a lot of casualties on the Romans but in turn suffered very heavy defeats. They were on the verge of being crushed when Agricolla was recalled before he could finish them , off and later Severus died before he could .
They didn't seen to think that Ireland was worth invading . Although there were no treaties and Ireland wasn't a Roman client state there was contact with trading and some raiding by the Irish . The Romans seem to have had influence in Ireland perhaps through having favoured trading partners . Ireland seems to have been quite stable during the Roman occupation of Britain and went through a long period of instability after the Legions were withdrawn .
Too expensive and not really interesting. There was nothing of value there. Both locations were populated by hostile "barbarians". Finally, the size of Ireland or Scotland was not fully known, so people in charge didn't want to waste precious military resources.
On the other hand Roman armies were not that great. They failed to take over German lands, which were not that extensive. Instead of holding super expensive frontiers it would be logical to expand and take over sparsely populated forests of central Europe. But Romans couldn't for whatever reason.
Yeah something like that. In Scotland the Romans faced a group of tribes known as the Picts or painted people. These people often painted blue dye on their faces and bodies and would charge into battle naked. I suppose the Romans thought they were too wild and not capable of being "civilised".
The Irish clans did have contact with the Romans and wearing Roman clothes became fashionable. I think the Romans built a fort near Dublin so as to be able to scout out the local area. Rumours had been going around that the Irish were all cannibals which would have intimidated soldiers and military commanders considering an invasion.